Textbook Mapping — OpenStax Precalculus 2e
This course maps to specific chapters of OpenStax Precalculus 2e by Jay Abramson. The OpenStax text covers both college algebra (Ch 1-4, 9-11) and trigonometry/pre-calculus (Ch 5-8, 12). Our 8-chapter course structure draws primarily from Ch 5-8 with supplementary material.
OpenStax Chapter Overview
| OpenStax Ch | Title | Our Course | Status |
|---|---|---|---|
1 |
Functions |
Review (College Algebra Ch 2) |
Covered |
2 |
Linear Functions |
Review (College Algebra Ch 2) |
Covered |
3 |
Polynomial and Rational Functions |
Review (College Algebra Ch 3) |
Covered |
4 |
Exponential and Logarithmic Functions |
Review (College Algebra Ch 4) |
Covered |
5 |
Trigonometric Functions |
Our Ch 1: Trig Functions |
Not Started |
6 |
Periodic Functions |
Our Ch 2: Trig Graphs |
Not Started |
7 |
Trigonometric Identities and Equations |
Our Ch 3 + Ch 4 |
Not Started |
8 |
Further Applications of Trigonometry |
Our Ch 5 + Ch 6 (partial) |
Not Started |
9 |
Systems of Equations and Inequalities |
Review (College Algebra Ch 5) |
Covered |
10 |
Analytic Geometry |
Review (College Algebra Ch 7) + Our Ch 7 |
Partial |
11 |
Sequences, Probability, Counting |
Review (College Algebra Ch 8) |
Covered |
12 |
Introduction to Calculus |
Our Ch 8: Limits Preview |
Not Started |
Detailed Section Mapping
Our Chapter 1: Trigonometric Functions → OpenStax Ch 5
| Our Section | Topic | OpenStax Section |
|---|---|---|
1.1 |
Angles and Measurement |
5.1 Angles |
1.2 |
Unit Circle |
5.2 Unit Circle: Sine and Cosine Functions |
1.3 |
Right Triangle Trig |
5.3 The Other Trigonometric Functions |
1.4 |
Trig Functions of Any Angle |
5.2 + 5.3 (extended) |
1.5 |
Reference Angles |
5.2 (reference angles subsection) |
1.6 |
Inverse Trig Functions |
5.3 + supplementary |
Our Chapter 2: Graphs of Trig Functions → OpenStax Ch 6
| Our Section | Topic | OpenStax Section |
|---|---|---|
2.1 |
Graphs of Sine and Cosine |
6.1 Graphs of the Sine and Cosine Functions |
2.2 |
Graphs of Other Trig Functions |
6.2 Graphs of the Other Trigonometric Functions |
2.3 |
Inverse Trig Graphs |
6.3 Inverse Trigonometric Functions |
2.4 |
Transformations |
6.1-6.2 (transformation subsections) |
2.5 |
Applications of Sinusoidal Functions |
6.1 (modeling subsection) + supplementary |
Our Chapter 3: Trigonometric Identities → OpenStax Ch 7 (first half)
| Our Section | Topic | OpenStax Section |
|---|---|---|
3.1 |
Fundamental Identities |
7.1 Solving Trigonometric Equations with Identities |
3.2 |
Sum and Difference Formulas |
7.2 Sum and Difference Identities |
3.3 |
Double and Half Angle |
7.3 Double-Angle, Half-Angle, and Reduction Formulas |
3.4 |
Product-to-Sum |
7.4 Sum-to-Product and Product-to-Sum Formulas |
3.5 |
Verifying Identities |
7.1 (verification techniques) |
Our Chapter 4: Trigonometric Equations → OpenStax Ch 7 (second half)
| Our Section | Topic | OpenStax Section |
|---|---|---|
4.1 |
Basic Trig Equations |
7.5 Solving Trigonometric Equations |
4.2 |
Advanced Trig Equations |
7.6 Modeling with Trigonometric Equations |
4.3 |
Equations with Identities |
7.5 (identity-based solving) |
4.4 |
Applications |
7.6 + supplementary |
Our Chapter 5: Applications of Trigonometry → OpenStax Ch 8
| Our Section | Topic | OpenStax Section |
|---|---|---|
5.1 |
Law of Sines |
8.1 Non-right Triangles: Law of Sines |
5.2 |
Law of Cosines |
8.2 Non-right Triangles: Law of Cosines |
5.3 |
Area of Triangles |
8.1-8.2 (area subsections) |
5.4 |
Vectors Introduction |
8.8 Vectors |
5.5 |
Dot Product |
8.8 (dot product subsection) + supplementary |
Our Chapter 6: Polar & Parametric → OpenStax Ch 8
| Our Section | Topic | OpenStax Section |
|---|---|---|
6.1 |
Polar Coordinates |
8.3 Polar Coordinates |
6.2 |
Polar Graphs |
8.4 Polar Coordinates: Graphs |
6.3 |
Polar Form of Complex Numbers |
8.5 Polar Form of Complex Numbers |
6.4 |
Parametric Equations |
8.6 Parametric Equations |
Our Chapter 7: Conic Sections in Polar Form → OpenStax Ch 8 + Ch 10
| Our Section | Topic | OpenStax Section |
|---|---|---|
7.1 |
Conics in Polar Form |
8.7 Parametric Equations: Graphs + 10.5 Conic Sections in Polar Coordinates |
7.2 |
Rotation of Axes |
10.4 Rotation of Axes |
7.3 |
Review of Conics |
10.1-10.3 (unified review) |
Our Chapter 8: Introduction to Limits → OpenStax Ch 12
| Our Section | Topic | OpenStax Section |
|---|---|---|
8.1 |
Concept of a Limit |
12.1 Finding Limits: Numerical and Graphical Approaches |
8.2 |
Limit Computation |
12.2 Finding Limits: Properties of Limits + 12.3 Continuity |
8.3 |
Continuity Preview |
12.3 Continuity + 12.4 Derivatives |
Notes
-
OpenStax Ch 7 is split across our Ch 3 (identities) and Ch 4 (equations) for pedagogical clarity
-
OpenStax Ch 8 is large — it feeds our Ch 5, Ch 6, and part of Ch 7
-
OpenStax Ch 10 (Analytic Geometry) overlaps with College Algebra Ch 7 for conics in rectangular form; our Ch 7 covers only the polar form extension
-
OpenStax Ch 12 provides a calculus preview — our Ch 8 covers limits only, not the derivative introduction in 12.4